1- Might the t- forms be best considered/analysed as auxiliaries?
Response: that is quite possible. I just hadn’t really nailed down the analysis like this. Verb sequences like this do often seem to grammaticalise into auxiliaries. However, ‘auxiliary’ is a fairly non-descriptive and wide category, so I’m not sure whether it helps us beyond giving a category to the word.
2- Obligation doesn’t fit well with Imperfective aspect. Perhaps it’s best seeing all these semantic categories as being potential (rather than actual).
Response: it seemed odd to me to put the habituals and some past/definite events in a ‘potential’ category, but I had considered at an early stage whether this might be marking realis/irrealis distinction. Possibly this is an aspect/mode complex. More examples from natural texts would be helpful to narrow this down.

Roger Blench:
3- Should the schewa (ạ) and a not be considered rather as the same central vowel or a nasal just distinguished by tone?
Response: I would need to look into this more. They seem to be distinguished, but that may just be a perception of MT speakers and me.
4- Duka seems to show a similar t- form based on the preliminary dictionary.